GCF of 920/25, 312/8655
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 920/25, 312/8655 i.e 8/43275 easily. The following is the detailed procedure to determine the greatest common factor of fractions 920/25, 312/8655.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
What is the GCF of 920/25,312/8655?
Given fractions are 920/25,312/8655
To find the GCF of fractions, we have to find the GCF of numerator numbers and LCM of denominator numbers. Its formula is given by
GCF of Fraction = Greatest Common Factor of Numerator/Least Common Multiple of Denominators
In the fractions 920/25,312/8655, numerators are 920,312
Denominators are 25,8655
The GCF of 920,312 is 8 .
LCM of 25,8655 is 43275.
The greatest common factor of 920/25,312/8655 = [GCF of 920,312]/[LCM of 25,8655]= 8/43275
Therefore, the GCF of 920/25,312/8655 is 8/43275.
To find the highest common factor of 920,312, we have to find the factors of both numbers and list the highest common factor.
The factors of 920 are 1, 2, 4, 5, 8, 10, 20, 23, 40, 46, 92, 115, 184, 230, 460, 920
The factors of 312 are 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312
The HCF of 920,312 is 8.
Lets's calculate GCF of 920,312
| 2 | 920, 312 |
| 2 | 460, 156 |
| 2 | 230, 78 |
| 115, 39 |
∴ So the GCF of the given numbers is 2 x 2 x 2 = 8
Greatest Common Factor of 920,312 By Matching Biggest Common Factor Method
Now, list down the factors of 920
:1,2,4,5,8,10,20,23,40,46,92,115,184,230,460,920
Now, list down the factors of 312
:1,2,3,4,6,8,12,13,24,26,39,52,78,104,156,312
Greatest Common Factor
We found the factors 920,312 . The biggest common factor number is the GCF number.
So the greatest common factor 920,312 is 8.
Lets's calculate LCM of 25,8655
| 5 | 25, 8655 |
| 5, 1731 |
∴ So the LCM of the given numbers is 5 x 5 x 1731 = 43275
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 8/43275
Therefore, the GCF of Fractions 920/25,312/8655 is 8/43275
Least Common Multiple of 25,8655 with GCF Formula
The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).
We need to calculate greatest common factor of 25,8655 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(25,8655) = 5
common factors(in case of two or more numbers have common factors) = 1
GCF(25,8655) x common factors =5 x 1 = 5
LCM(25,8655) = ( 25 × 8655 ) / 5
LCM(25,8655) = 216375 / 5
LCM(25,8655) = 43275
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FAQs on GCF of Fractions of 920/25, 312/8655
1. What is the HCF of 920,312?
The HCF of 920,312 is 8
2. What is the GCF of a fraction?
The GCF of a fraction is defined as the greatest fraction that divides exactly into 2 or more fractions.
3. How to find GCF in Fractions?
Answer: GCF of fractions can be found using the simple formula GCF of Fractions = GCF of Numerators/LCM of Denominators.
4. What is the GCF of Fractions for 920/25, 312/8655?
Answer: GCF of Numerators as per given numbers 920/25, 312/8655 is
GCF of Numerators i.e. for 920,312 is 8
LCM of denominators i.e. for 25,8655 is 43275.
Thus, GCF of Fractions is 8/43275.Finally, GCF of Fractions for 920/25, 312/8655 is 8/43275.